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This dissertation is a systematic theoretical effort to investigate the low-energy properties of random antiferromagnetic quantum spin-1/2 systems beyond one dimension. We use the celebrated real space renormalization group (RSRG) technique developed by Dasgupta, Ma, and Hu to understand the static and dynamic properties of random antiferromagnetic spin-1/2 ladders and weakly coupled random antiferromagnetic spin-1/2 chains. Pure antiferromagnetic spin-1/2 ladders are known to be in the spin liquid phase with a ¯nite energy gap in the excitation spectrum and a short range spin-spin correlation. We are interested in investigating the nature of these systems when disorder, controlled by bond randomness and the presence of impurities, is introduced. Using real-space renormalization group method we are able to find that when disorder comes from bond randomness only, the system flows into a Griffith phase which is characterized by non-universal diverging spin susceptibility and short-range spin-spin correlation. When impurities with spin 0 or 1 are introduced into the system, the system flows into a different fixed point which is controlled by large effective spins whose susceptibility is characterized by a universal Curie-like 1=T behavior. This conclusion holds for any impurities with integer spin. We also study the low-energy collective excitations and dynamical response functions of weakly coupled random antiferromagnetic spin-1/2 chains at low temperature whose low energy properties are governed by the strong-randomness fixed point. By combining RSRG technique to tackle the intrachain couplings and Random Phase Approximation (RPA) formalism for the interchain couplings, we show that the system supports collective spin wave excitations with linear dispersions and calculate the spin wave velocity in terms of microscopic parameters of the chain. Our result agrees with the measured dispersion for Zn-doped CuGeO3 where it shows a linear dispersion along the chain. We predict the spectra weight within RPA which can be qualitatively compared to the scattering intensity in the Inelastic Neutron Scattering experiment.
A Dissertation Submitted to the Department of Physics in Partial FulﬁLlment of the Requirements for the Degree of Doctor of Philosophy.
Includes bibliographical references.
Florida State University
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